-
作者：Shi, Chengchun; Song, Rui; Chen, Zhao; Li, Runze
作者单位：North Carolina State University; Fudan University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：This paper is concerned with testing linear hypotheses in high dimensional generalized linear models. To deal with linear hypotheses, we first propose the constrained partial regularization method and study its statistical properties. We further introduce an algorithm for solving regularization problems with folded-concave penalty functions and linear constraints. To test linear hypotheses, we propose a partial penalized likelihood ratio test, a partial penalized score test and a partial penal...
-
作者：Ierkens, Joris B.; Fearnhead, Paul; Roberts, Gareth
作者单位：Delft University of Technology; Delft University of Technology; Lancaster University; University of Warwick
摘要：Standard MCMC methods can scale poorly to big data settings due to the need to evaluate the likelihood at each iteration. There have been a number of approximate MCMC algorithms that use sub-sampling ideas to reduce this computational burden, but with the drawback that these algorithms no longer target the true posterior distribution. We introduce a new family of Monte Carlo methods based upon a multidimensional version of the Zig-Zag process of [Ann. Appl. Probab. 27 (2017) 846-882], a contin...
-
作者：Banerjee, Moulinath; Durot, Cecile; Sen, Bodhisattva
作者单位：University of Michigan System; University of Michigan; Columbia University
摘要：We study how the divide and conquer principle works in non-standard problems where rates of convergence are typically slower than root n and limit distributions are non-Gaussian, and provide a detailed treatment for a variety of important and well-studied problems involving nonparametric estimation of a monotone function. We find that for a fixed model, the pooled estimator, obtained by averaging nonstandard estimates across mutually exclusive subsamples, outperforms the nonstandard monotonici...
-
作者：Monard, Francois; Nickl, Richard; Paternain, Gabriel P.
作者单位：University of California System; University of California Santa Cruz; University of Cambridge
摘要：We consider the statistical inverse problem of recovering a function f : M -> R, where M is a smooth compact Riemannian manifold with boundary, from measurements of general X-ray transforms I-a(f) of f, corrupted by additive Gaussian noise. For M equal to the unit disk with flat geometry and a = 0 this reduces to the standard Radon transform, but our general setting allows for anisotropic media M and can further model local attenuation effects-both highly relevant in practical imaging problems...
-
作者：Enikeeva, Farida; Harchaoui, Zaid
作者单位：Universite de Poitiers; Centre National de la Recherche Scientifique (CNRS); Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS; University of Washington; University of Washington Seattle
摘要：We consider the problem of detecting a change in mean in a sequence of high-dimensional Gaussian vectors. The change in mean may be occurring simultaneously in an unknown subset components. We propose a hypothesis test to detect the presence of a change-point and establish the detection boundary in different regimes under the assumption that the dimension tends to infinity and the length of the sequence grows with the dimension. A remarkable feature of the proposed test is that it does not req...
-
作者：Truquet, Lionel
作者单位：Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI); Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI)
摘要：A primary motivation of this contribution is to define new locally stationary Markov models for categorical or integer-valued data. For this initial purpose, we propose a new general approach for dealing with time-inhomogeneity that extends the local stationarity notion developed in the time series literature. We also introduce a probabilistic framework which is very flexible and allows us to consider a much larger class of Markov chain models on arbitrary state spaces, including most of the l...
-
作者：Deligiannidis, George; Bouchard-Cote, Alexandre; Doucet, Arnaud
作者单位：University of Oxford; University of British Columbia
摘要：Nonreversible Markov chain Monte Carlo schemes based on piecewise deterministic Markov processes have been recently introduced in applied probability, automatic control, physics and statistics. Although these algorithms demonstrate experimentally good performance and are accordingly increasingly used in a wide range of applications, geometric ergodicity results for such schemes have only been established so far under very restrictive assumptions. We give here verifiable conditions on the targe...
-
作者：Drton, Mathias; Fox, Christopher; Kaeufl, Andreas; Pouliot, Guillaume
作者单位：University of Washington; University of Washington Seattle; University of Copenhagen; University of Chicago; University of Augsburg; University of Chicago; Universite de Montreal; Polytechnique Montreal
摘要：Linear structural equation models postulate noisy linear relationships between variables of interest. Each model corresponds to a path diagram, which is a mixed graph with directed edges that encode the domains of the linear functions and bidirected edges that indicate possible correlations among noise terms. Using this graphical representation, we determine the maximum likelihood threshold, that is, the minimum sample size at which the likelihood function of a Gaussian structural equation mod...
-
作者：Petersen, Alexander; Mueller, Hans-Georg
作者单位：University of California System; University of California Santa Barbara; University of California System; University of California Davis
摘要：Increasingly, statisticians are faced with the task of analyzing complex data that are non-Euclidean and specifically do not lie in a vector space. To address the need for statistical methods for such data, we introduce the concept of Frechet regression. This is a general approach to regression when responses are complex random objects in a metric space and predictors are in R-p, achieved by extending the classical concept of a Frechet mean to the notion of a conditional Frechet mean. We devel...
-
作者：Cao, Xuan; Khare, Kshitij; Ghosh, Malay
作者单位：State University System of Florida; University of Florida
摘要：Covariance estimation and selection for high-dimensional multivariate datasets is a fundamental problem in modern statistics. Gaussian directed acyclic graph (DAG) models are a popular class of models used for this purpose. Gaussian DAG models introduce sparsity in the Cholesky factor of the inverse covariance matrix, and the sparsity pattern in turn corresponds to specific conditional independence assumptions on the underlying variables. A variety of priors have been developed in recent years...
